Introduction of the Navier-Strokes equations and the flow modeling in the hydrodynamic scale. The derivation of the Boltzmann equation in the kinetic scale. The basic mathematical analysis of the Chapman-Enskog expansion and the numerical methods for the Boltzmann equation. The multiscale modeling from the kinetic to the hydrodynamic scales and the discretized governing equations. The study of non-equilibrium transport phenomena in gas dynamics, radiative and heat transfer, and plasma physics.